Symmetry and Nonexistence of Positive Solutions for a Fractional Laplacion System with Coupled Terms

In this paper, we study the problem for a nonlinear elliptic system involving fractional Laplacion: (equation 1.1) where 0 < α, β < 2, p, q > 0 and max{p, q} ≥ 1, α + γ > 0, β + τ > 0, n ≥ 2. First of all, while in the subcritical case, i.e. n + α + γ − p(n − α) − (q + 1)(n − β) > 0, n + β + τ − (p + 1)(n − α) − q(n − β) > 0, we prove the nonexistence of positive solution for the above system in R n . Moreover, though Doubling Lemma to obtain the singularity estimates of the positive solution on bounded domain Ω. In addition, while in the critical case, i.e. n+α+γ −p(n−α)−(q + 1)(n−β) = 0, n+β +τ −(p+ 1)(n−α)−q(n−β) = 0, we show that the positive solution of above system are radical symmetric and decreasing about some point by using the method of Moving planes in Rn Mathematics Subject Classification (2020): 35R11, 35A10, 35B06.

Metal Coordination Properties of a Chromophoric Desferrioxamine (DFO) Derivative: Insight on the Coordination Stoichiometry and Thermodynamic Stability of Zr4+ Complexes

Desferrioxamine (DFO) is the current “gold standard” chelator for 89Zr4+, which is used to label monoclonal antibodies for applications in immunopositron emission tomography. Recently, controversial data have been reported regarding the speciation and the stability of the complexes formed by DFO with Zr4+ in solution. To shed some light on this point, we studied the coordination properties in solution ofa chromophoric DFO derivative bearing a substituted pyrimidine residue (DFO–Pm) toward several metal ions (Zr4+, Cu2+, Zn2+, Mg2+, Ca2+, Na+, K+). Potentiometric titrations showed that DFO–Pm and pristine DFO form complexes with very similar stoichiometry and stability. DFO–Pm, which can consequently be taken as a model system for DFO, provides a photochemical response to metal coordination that can be used to further define the complexes formed. In the critical case of Zr4+, spectrophotometric measurements allowed the verification of the formation of 1:1 and 2:3 complexes that, together with 2:2 complexes form the coordination model that was obtained through the use of our potentiometric measurements. Additionally, mass spectrometry measurements verified the formation of 1:1 and 2:3 complexes and showed that 1:2 species can be easily generated through the fragmentation of the 2:3 species. In conclusion, the results obtained with DFO–Pm validate the complexation model of Zr4+/DFO composed of 1:1, 2:2, and 2:3 metal-to-ligand complexes. Convergences and conflicts with other works are addressed.

“She Started Wearing Men’s Clothing and Acting More Masculine"

This paper examines two examples of archival visual information with potentially transgender and non-binary representation to interrogate the descriptive challenges latent within such materials. By using gender theory and queer historiography, this paper deploys a critical case study to consider the particularities of naming gender when contextual evidence provides little to no authoritative guidance. By talking through the way gender makes itself visible within visual information, the paper guides readers through the way transgender or non-binary identity might exist within both pieces of visual information. The paper then provides suggestions on how to provide respectful and inclusive descriptive records that attend to the complexities of a still-evolving queer history. By offering both a statement on the impossibility of naming identity within intersecting forms of queer embodiment alongside reference points for methods of discussing potential gendered identities, the paper offers practical approaches to describing transgender and non-binary identities for information professionals.

The role of humour and laughter therapy in decreasing caregiver burden among carers of a person living with dementia- A case study

Gibbs (1988) reflective cycle was employed to explore a critical case study involving a senior citizen with dementia and measures to reduce caregiver burden by humour and laughter therapy. This experience highlights key themes of caregiver burden-reduction measures through humour and laughter. This problem is discussed in relation to lack of awareness about measures to reduce caregiver burden arising due to caretaking of a person with dementia. Inclusion of this therapy as a non-pharmacological method of stress management, could be useful in the guidelines for dementia care. Therefore, it is important to include training to all caregivers at home and care home setting to address the issue of caregiver burden.

Preferences in Between: Moderates in the Catalan Secessionist Conflict

Recent research on territorial preferences focuses on explaining who supports or opposes independence. However, this research overlooks the relevance of an “intermediate” category of citizens who may oppose the territorial status quo of a sub-state territory but not support independence. We use evidence from the critical case of Catalonia to illustrate the relevance of individuals with such preferences for policies and outcomes highly relevant to secessionist conflicts. We present four sets of findings using two-wave panel data from December 2017 (just prior to the December regional elections when Catalan independence was the most salient and contentious issue) and September 2018. First, we find that a sizable plurality within Catalonia supports greater autonomy short of independence; conventional sociodemographic variables explaining support for independence do not strongly account for this preference. Second, such pro-autonomy individuals have considerably more intermediate attitudes regarding the key “on the ground” actions that the Spanish and Catalan governments pursued during the crucial independence drive in 2017. They were more opposed than pro-independence individuals to the unilateral independence efforts, and more opposed than pro-status quo individuals to the Spanish government’s actions to counter these efforts. Third, they expressed emotions around the secessionist conflict similar to pro-status quo individuals. Finally, using an embedded survey experiment, we find that pro-autonomy individuals are more trusting of both the central and regional governments regarding their abiding by an agreement to resolve the conflict, and are less easily “polarized” through priming. Overall, these findings indicate the importance of further analyzing individuals with intermediate territorial views in secessionist conflicts.

Solvability for time-fractional semilinear parabolic equations with singular initial data

We discuss the existence and nonexistence of a local and global-in-time solution to the fractional problem $$ ¥begin{cases} ¥partial_t^{¥alpha}u=¥Delta u+f(u) & x¥in¥Omega,¥ 01$ one has $|f(¥xi)-f(¥eta)|¥le C(1+|¥xi|+|¥eta|)^{p-1}|¥xi-¥eta|$ for all $¥xi, ¥eta¥in ¥R$. Particular attention is paid to the doubly critical case $(p,r)=(1+2/N,1)$.

Classification of nonnegative solutions to static Schrödinger–Hartree–Maxwell system involving the fractional Laplacian

This paper is mainly concerned with the following semi-linear system involving the fractional Laplacian: $$ \textstyle\begin{cases} (-\Delta )^{\frac{\alpha }{2}}u(x)= (\frac{1}{ \vert \cdot \vert ^{\sigma }} \ast v^{p_{1}} )v^{p_{2}}(x), \quad x\in \mathbb{R}^{n}, \\ (-\Delta )^{\frac{\alpha }{2}}v(x)= (\frac{1}{ \vert \cdot \vert ^{\sigma }} \ast u^{q_{1}} )u^{q_{2}}(x), \quad x\in \mathbb{R}^{n}, \\ u(x)\geq 0,\quad\quad v(x)\geq 0, \quad x\in \mathbb{R}^{n}, \end{cases} $$ { ( − Δ ) α 2 u ( x ) = ( 1 | ⋅ | σ ∗ v p 1 ) v p 2 ( x ) , x ∈ R n , ( − Δ ) α 2 v ( x ) = ( 1 | ⋅ | σ ∗ u q 1 ) u q 2 ( x ) , x ∈ R n , u ( x ) ≥ 0 , v ( x ) ≥ 0 , x ∈ R n , where $0<\alpha \leq 2$ 0 < α ≤ 2 , $n\geq 2$ n ≥ 2 , $0<\sigma <n$ 0 < σ < n , and $0< p_{1}, q_{1}\leq \frac{2n-\sigma }{n-\alpha }$ 0 < p 1 , q 1 ≤ 2 n − σ n − α , $0< p_{2}, q_{2}\leq \frac{n+\alpha -\sigma }{n-\alpha }$ 0 < p 2 , q 2 ≤ n + α − σ n − α . Applying a variant (for nonlocal nonlinearity) of the direct method of moving spheres for fractional Laplacians, which was developed by W. Chen, Y. Li, and R. Zhang (J. Funct. Anal. 272(10):4131–4157, 2017), we derive the explicit forms for positive solution $(u,v)$ ( u , v ) in the critical case and nonexistence of positive solutions in the subcritical cases.

A general blow-up result for a degenerate hyperbolic inequality in an exterior domain

In this paper, we consider a degenerate hyperbolic inequality in an exterior domain under three types of boundary conditions: Dirichlet-type, Neumann-type, and Robin-type boundary conditions. Using a unified approach, we show that all the considered problems have the same Fujita critical exponent. Moreover, we answer some open questions from the literature regarding the critical case.